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Mathematical medallist: Seducing CEOs and socialists

By Jacob Aron

Cédric Villani‘s mission to tell the world what it means to be a mathematician began when he won a Fields medal, often called the Nobel prize of mathematics. Director of the Henri Poincaré Institute in Paris, France, he studies kinetic theory, the mathematical interpretation of thermodynamic concepts like entropy, and was one of four mathematicians under 40 who won the medal last year. New Scientist caught up with him at a public talk at the London Mathematical Society.

It’s almost a year since you won the Fields medal – what’s changed?This year has been completely different. Basically I have done no research. I have given talks, talks, talks everywhere, with politicians, journalists, school kids, university students, all kinds of people. Each time it has been a very interesting experience, but I have given more than 100 talks during the past year. Some weeks I have had a different talk every day to prepare.

How did you convey your ideas to such different audiences?When I gave a talk in front of a rally of the extreme left, I did not give the same talk as I did in front of a group of CEOs, although there were a lot of things that resonated with me in both contexts. Each time I tried to think&colon; “In my work, what is the resemblance with them?” For the extreme left I emphasised the values of internationalism and idealism, which are the basis of science. With the CEOs, I focussed on the daring part of my work, the fact that as researchers we are adventurers and try to explore and conquer, and the fact that as the director of an institute I am a bit like a CEO. I discovered that in all of these worlds that I was not familiar with, I could always find a way to connect.

Was giving all these talks enjoyable, or were you worried about being away from your research?When you feel that small frustration that you don’t work enough, it’s a good thing, it motivates you. It’s much worse when you have too much time and you don’t find the motivation. Yes, I am longing for more time for research. But I had this idea that I was fulfilling my mission of bridging worlds and acting as a figurehead for a community which is very poorly known and under-represented.

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Why do you want to raise the profile of mathematicians?People don’t know about mathematicians. Some journalists ask me&colon; “What is 523 multiplied by 300?” like this is what a mathematician does. Others seem to think that we sit around doing computations, with the fastest one winning. This is the idea many people have of mathematicians. But mathematics is not just about computation, it’s about the world we live in and concepts.

Kinetic theory been around for over 100 years. Is it surprising there are still things to discover?I think this is the usual fate of the most important branches of mathematics. When we study the real world, gosh, it is so messy that we are light years away from understanding it – we understand tiny islands. In the case of kinetic theory, it’s an island that’s not so tiny. Boltzmann’s equation [which forms the basis of kinetic theory] is very rich in ideas and at the same time it’s a real equation that engineers use.

Do you like that there are applications for the mathematics you do, or do you prefer abstract puzzles?When I started my PhD, I wanted something that had real applications. Now it’s a bit different. I like the fact that there are applications, but it’s not the most important thing to me. On the other hand, the fact that it is rooted in the real world contributes to the aesthetic of the equation – I find the problem is more beautiful if there is a root in reality.

What is the biggest problem facing mathematics at the moment?The question can be understood in several ways. The most visible of the mathematical enigmas is the Riemann hypothesis [which offers a way to predict the occurrence of prime numbers]. The guy who solves this will immediately become the most famous mathematician of the century. It’s such a beautiful problem, so simple, and there is some romantic flavour around Riemann, his short life and tragic destiny [Bernhard Riemann died of tuberculosis aged 39].

More generally, mathematics is doing extremely well at the moment and we are at a period where past demons have disappeared. There was a time where there was this huge gap between pure and applied mathematics. Now it’s quite the contrary, with all mathematicians kind of agreeing there’s a continuum.

The links between computer science and mathematics are stronger than ever. The whole aesthetics of mathematics is being shaped by this interaction. Physicists and mathematics go very well together also, and the development of supercomputing gives new possibilities, new insights and new ways to test things, so it’s a very exciting time.